Question

`int (cos4x)/(sin2x + cos2x)dx` = ______.

Options

• sin 2x + cos 2x + c

• `1/2(sin 2x + cos 2x) + c`

• 2(sin 2x + cos 2x) + c

• 2 sin 4x + c

Answer 1

`int (cos4x)/(sin2x + cos2x)dx` = `underlinebb(1/2 (sin  2x + cos  2x) + c)`.

Explanation:

`int (cos^2 2x - sin^2 2x)/(sin2x + cos2x)dx`

= `int ((cos2x + sin2x)(cos2x - sin2x)dx)/((sin2x + cos 2x))`

= `int (cos2x - sin2x)dx`

= `1/2(sin2x + cos2x) + c`